Each camera may always keep the same resolution?
As far as I know, the answer is no.

The resolution is a global property used by all camera objects in the scene. 

One way to work around this is to create a new scene:


Create a new scene with Link Objects in Info > Header by pressing the + button:



This will make copy the current scene into new one and make object mesh data and transforms linked from one scene to another, so if you move or edit an object in one scene, the corresponding object in another scene will move to match it.
Set the other camera as active in the new scene (CtrlNumpad 0)
Change the resolution in the new scene.
To render, select the scene which has the active camera and resolution you want and press F12


Note that it is probably simpler and easier to set the resolution manually when you render.